In the field of computer graphics, to compensate for input/output (I/O) characteristics, image information generally needs to be corrected. To input image information, a given input device such as a scanner has a particular set of input characteristics for red, green and blue (RGB). For example, certain scanners are more sensitive to a red input than a green input while certain other scanners do not have the above input characteristics. Due to these device dependent characteristics, the RGB image information scanned by one scanner would not be necessarily compatible with other RGB information inputted by another scanner. Similarly, to output an image information, a given printer has a particular set of output characteristics for cyan, magenta, yellow and black (CMYK), and due to these characteristics, the image information would not be compatible with other CMYK image information to be outputted by a different printer. Because of the above described device dependent characteristics, these input and output information are corrected so as to make them compatible between devices.
In addition to the above described I/O device dependent characteristics, color toner used by a printer also influences an image outputted on an image-carrying medium. In general, to render an image on a sheet of paper, four color toner including cyan, magenta, yellow and black are combined to output a specified color. However, due to the chemical composition, some color toner are not generally pure in their colors. In other words, as shown in FIG. 1, although the cyan toner has the strongest y output intensity in cyan for any given x input value, the cyan toner also has some magenta and yellow output intensities. Similarly, as shown in FIG. 2, the magenta toner is generally not pure and also renders some yellow and cyan when it is applied on an image-carrying medium. On the other hand, the yellow toner is substantially pure and renders insignificant cyan and magenta output intensities as shown in FIG. 3. Due to the above described color specific toner characteristics, when these three colors of toner are applied together, they do not render a uniform intensity as shown in FIG. 4. In order to fine tune the color balance in the output image, each of the above color toner outputs needs to be adjusted.
In order to correct the image information according to the above described characteristics of an I/O device as well as toner, a correction curve was used in prior art. A typical correction curve was generated by a function whose input and output values had predetermined ranges. The functions included gamma functions such as y=x.sup..gamma. where .gamma. is a selected constant, and both x and y range between 0 and 1. The range between 0 and 1 for the inputs or the outputs was correlated to 64 (6 bits) or 256 (8 bits) color intensity levels. For a given input value x, which might be a RGB value or a CMYK value, a particular corrected output value y was obtained based upon a predetermined function. However, this type of gamma correction functions was rather limited by a single constant parameter which generated a rather uniform curvature. Other prior art gamma functions involved polynomial equations as disclosed by Japanese Patent No 63-2462 and Japanese Patent No 6-105154.
Japanese Patent No 63-2462 discloses a method and a system of correcting image information by a series of adjustments to a curve generated by a polynomial such as a quadratic or cubic equation. The adjustments include a rotation of the curve by a predetermined angle .theta. about the origin and a shift of the rotated curve by a predetermined amount in either or both along the X and Y axes. Although these adjustments to the gamma correction curve provide some degree of flexibility, the total number of the parameters necessary for the correction is undesirably large. As a result, additional hardware such as registers and memory is required.
To reduce the number of parameters, Japanese Patent No. 6-105154 (the 154 reference) discloses a Murayama-Bezier (MB) curve as a gamma correction curve. The MB curve is expressed as follows: EQU y=cx(1-x).sup.2 +(3-d) (1-x)x.sup.2 +x.sup.3
where 0.ltoreq.x.ltoreq.1. The curvature of the above MB curve is adjusted by a pair of parameters c and d. The parameter c determines the slope of a tangential line at the starting point (0,0) while the other parameter d determines the slope of a tangential line at the ending point (1,1).
In addition to the above described two-parameter adjustment, the 154 reference also discloses the four-parameter adjustment. For a specified x value, without changing the curvatures specified by c and d (here expressed as c.sub.1 and d.sub.1), the above MB curve is further adjusted by another pair of parameters c.sub.2 and d.sub.2, which are defined as follows: c=c.sub.1 +C.sub.2 (1-x) x and d=d.sub.1 +d.sub.2 (1-x) x. Thus, at a point specified by a x value, the curve is further modified in the y direction without modifying the above described original starting and ending slopes of the curve specified by c.sub.1 and d.sub.1.
In general, due to the complex nature of the corrections, the above described correction has been performed using pre-calculated tables. Since the correction process requires complex equations and a number of parameters, it is impractical to calculate the correction data on the fly during its correction process. Although the pre-calculated table look-up process is more efficient, it is rather limited and lacking flexibility in correcting image information. Furthermore, to handle a large number of variations in the device as well as toner characteristics for a wide range of input and output values, a voluminous amount of pre-calculated data needs to be stored in the table memory. The amount of pre-calculated data is even larger when each color in a color system is independently corrected.
In the relevant prior art of color production technologies involving fax machines, copiers and printers, the image information has been generally corrected based upon the above described input or output characteristics using pre-calculated tables. This is because the prior art correction process is too complex to be performed on the fly or requires additional hardware. The correction process remains to be more efficient so that it is performed on the fly without the use of pre-calculated table.
In the relevant prior art, let alone, the color specific correction of the image information had not been performed. In general, all color components had been uniformly adjusted for the overall darkness or lightness of an outputted image. To allow the color specific adjustments of the image information, the correction process remains to be accomplished in a more efficient manner without sacrificing the system performance or without additional hardware. However, the color specific correction must be sufficiently flexible so that it can accommodate subtle color changes.